Abstract Simulations of the stress state in a region of discontinuously fractured rock revealed a strongly heterogeneous, self-organized stress distribution displaying internally balanced strains and corresponding energy storage. The explicit simulations follow a sequence which may be inferred to be irreversible and strongly dependent on interaction between fractures, implying a time-dependency. The state of the simulated reservoir displays a sensitivity characteristic of marginal stability. These numerical observations are compared with new and previous laboratory and field experiments spanning a wide range of size, stress magnitude and stress difference. The characteristics of the state of the simulated reservoir, laboratory samples and field behaviour are found to be consistent with the numerical predictions. A stress memory is evident. This supports previous conclusions that the concept of stress state as uniform, constant and resulting from averaged values of stresses or displacements, presently applied at remote and artificial boundaries, is grossly oversimplified and flawed.

Abstract The total grams of platinum group elements (PGE) in the Critical zone of the Bushveld when projected to the original horizontal and expressed as g/m 2 is relatively uniform for the Critical zone of the Bushveld Complex as a whole, varying from 157 to 171 g/m 2 in the western Bushveld and from 105 to 116 in the eastern Bushveld. However, in the interval from the top of the UG-2 to the top of the Merensky Reef, the northwestern Bushveld is twice as rich as the southwestern Bushveld, which is again significantly richer than the eastern Bushveld. This latter trend is also paralleled by the PGE "tenor factor" of the sulfides in samples close to the upper chromite seam of the Merensky Reef. These observations support the conclusions of Eales et al. ( 1988 , 1990 ), Scoon and Teigler ( 1994 ), and Maier and Teigler ( 1995 ) that a feeder for the Bushveld existed in the northwest during Merensky Reef time. Variation in the Cu/Pd ratio of sulfide-poor rocks suggests that the more mafic sequences in the interval between the top of the UG-2 and the Merensky Reef in the southwest Bushveld are due to influxes of an unusually PGE rich mafic magma across cumulates crystallizing from a magma with both plagioclase and orthopyroxene on the liquidus. The Merensky and Bastard reefs in this area are the culmination of these mafic influxes and their mixing with resident magma, albeit influxes that in these cases developed immiscible sulfide. The decrease in PGE tenor and increase in Cu/Pd ratio from near the upper chromite seam of the Merensky Reef upward into the overlying Merensky pyroxenite is consistent with the fractional segregation of sulfide from a PGE-enriched magma. A model is proposed for the emplacement of the Merensky Reef whereby influxes of magma spread away from the centers, mixing with resident magma, segregating sulfide, and becoming progressively depleted in PGE as they progressed. In general, the average PGE content of massive chromitites increases upward from the LG-1 to the UG-2/3. The LG-1 to LG-4 chromitites differ from those higher in the stratigraphy in having a much lower (Pt + Pd)/(Ru + Ir + Os) ratio. It has been suggested that the latter developed along with an immiscible magmatic sulfide liquid, while the former lacked this sulfide liquid. All chromitites are characterized by very high PGE/S ratios, and, in the case of those that contained original sulfide liquid sulfide, this is attributed to the original sulfide having been destroyed due to Fe entering the structure of cooling chromite, the f S2 rising, and the sulfur eventually being lost to the environment. Along with the sulfur, Cu and some of the Ni and Pd have also been lost, but not Pt, Rh, Ru, Ir, or Os. Ideas on the formation of Bushveld chromitites fall into two main groupings, those that maintain that they formed in situ ("onstage") and those that maintain that the chromite crystallized elsewhere ("offstage") and was introduced as a slurry. The problem that has puzzled researchers is what causes chromite to separate from a magma alone, without accompanying silicates. Observations reported here have shown that there are similar systematic variations in PGE profiles in the MG-3 and MG-4 chromitites in areas that are separated by 270 to 300 km and a progressive upward increase in V content in the UG-2 at Waterval shaft, all of which could not have resulted from introduction of the chromite in these units as a slurry; such observations argue strongly for an on-stage origin. An investigation has been made of spinel and orthopyroxene in a magma with the average composition of Critical zone magma, as a function of temperature, pressure, Cr 2 O 3 content, and H 2 O content and mixing with both fractionated mafic magma and felsic melt. Chromitites can form in situ if spinel crystallization precedes orthopyroxene on cooling. Accepting the usual maximum f o2 for the Bushveld as <QFM, MELTS modeling shows that this will only be the case if the Cr 2 O 3 content is >0.20 wt percent. Increasing total pressure has no effect on the f O2 at which spinel precedes orthopyroxene, indicating that increase in pressure will not precipitate a chromitite. The application of MELTS to mixtures of primary with 10 and 20 percent fractionated magma, and with admixtures of 20 percent average continental upper crust slightly increases the f O2 at which spinel precedes orthopyroxene, indicating that these mechanisms will not cause spinel to appear on the liquidus before orthopyroxene. It has been found that if the mixed magmas both have olivine (rather than orthopyroxene) along with spinel on the liquidus, a small amount of spinel will crystallize alone before it is joined by olivine; however, the modeling shows that those who have extended this concept to orthopyroxene—rather than olivine-rich magmas—are incorrect. The same is true of adding H 2 O. Calculations show that the limited amount of chromite that could form from a magma containing 0.25 percent Cr 2 O 3 at or below QFM means that a 70-cm-thick massive chromitite would have to seperate from a column of magma ≥1,000 m, supporting Eales's ( 2000 ) conclusion that the chromite in the Critical zone must have come from a volume of magma equal to many times the existing volume of cumulates. The whereabouts of the missing magma (the Critical zone cumulates are, on average, less than 2,000 m thick) is unknown, but it is suggested that part has exited the complex up its walls, leaving the Platreef and Sheba's Ridge deposits as witnesses to its passing—the pudding basin model. While contamination of Critical zone magma with a felsic melt will not promote chromite crystallization, it will also not prevent it at a given f O2 . Contamination with a melt of average upper crustal composition will, however, promote sulfide immiscibility, and it is proposed that this is the reason why some chromitites have developed with immiscible sulfide and are therefore rich in Pt and Pd, and others have not.